A274325 Number of partitions of n^5 into at most two parts.

1, 1, 17, 122, 513, 1563, 3889, 8404, 16385, 29525, 50001, 80526, 124417, 185647, 268913, 379688, 524289, 709929, 944785, 1238050, 1600001, 2042051, 2576817, 3218172, 3981313, 4882813, 5940689, 7174454, 8605185, 10255575, 12150001, 14314576, 16777217

Offset

0,3

Links

Colin Barker, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-9,5,5,-9,5,-1).

Formula

Coefficient of x^(n^5) in 1/((1-x)*(1-x^2)).

a(n) = A008619(n^5).

a(n) = (3 + (-1)^n + 2*n^5)/4.

a(n) = 5*a(n-1) - 9*a(n-2) + 5*a(n-3) + 5*a(n-4) - 9*a(n-5) + 5*a(n-6) - a(n-7) for n > 6.

G.f.: (1 - 4*x + 21*x^2 + 41*x^3 + 46*x^4 + 15*x^5) / ((1-x)^6*(1+x)).

E.g.f.: ((2 + x + 15*x^2 + 25*x^3 + 10*x^4 + x^5)*cosh(x) + (1 + x + 15*x^2 + 25*x^3 + 10*x^4 + x^5)*sinh(x))/2. - Stefano Spezia, Mar 17 2024

Maple

A274325:=n->(3+(-1)^n+2*n^5)/4: seq(A274325(n), n=0..50); # Wesley Ivan Hurt, Jun 25 2016

Mathematica

Table[(3+(-1)^n+2*n^5)/4, {n, 0, 50}] (* Wesley Ivan Hurt, Jun 25 2016 *)

Prog

(PARI)
\\ b(n) is the coefficient of x^n in the g.f. 1/((1-x)*(1-x^2)).
b(n) = (3+(-1)^n+2*n)/4
vector(50, n, n--; b(n^5))
(Magma) [(3+(-1)^n+2*n^5)/4 : n in [0..50]]; // Wesley Ivan Hurt, Jun 25 2016

Crossrefs

A subsequence of A008619.

Cf. A099392 (n^2), A274324 (n^3).

Sequence in context: A221329 A196806 A094944 * A108682 A031213 A196145

Adjacent sequences: A274322 A274323 A274324 * A274326 A274327 A274328

Keyword

nonn,easy

Author

Colin Barker, Jun 18 2016

Status

approved